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Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics

Sebastian Herr (2010)

Journées Équations aux dérivées partielles

This is a report on recent progress concerning the global well-posedness problem for energy-critical nonlinear Schrödinger equations posed on specific Riemannian manifolds $M$ with small initial data in $H^{1} (M)$ . The results include small data GWP for the quintic NLS in the case of the $3 d$ flat rational torus $M = 𝕋^{3}$ and small data GWP for the corresponding cubic NLS in the cases $M = ℝ^{2} \times 𝕋^{2}$ and $M = ℝ^{3} \times 𝕋$ . The main ingredients are bi-linear and tri-linear refinements of Strichartz estimates which obey the critical scaling, as well...

Équations de champ moyen pour la dynamique quantique d’un grand nombre de particules

Patrick Gérard (2003/2004)

Séminaire Bourbaki

L’objet de cet exposé est de montrer comment l’évolution de Schrödinger pour le problème à $N$ corps quantique est approchée, lorsque $N$ tend vers l’infini, dans un régime convenable, par une évolution non-linéaire en dimension trois d’espace. On traitera le cas des bosons, qui conduit à l’équation de Schrödinger-Poisson, et celui des fermions, qui débouche sur le système de Hartree-Fock.

Ergodicity for the stochastic complex Ginzburg–Landau equations

Cyril Odasso (2006)

Annales de l'I.H.P. Probabilités et statistiques

Error estimates for the Coupled Cluster method

Thorsten Rohwedder, Reinhold Schneider (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...

Evolution by the vortex filament equation of curves with a corner

Valeria Banica (2013)

Journées Équations aux dérivées partielles

In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in $ℝ^{3}$ and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...

Exact boundary controllability for higher order nonlinear Schrödinger equations with constant coefficients.

Ceballos V., Juan Carlos, Pavez F., Ricardo, Villagrán, Octavio Paulo Vera (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Exact solutions and symmetry operators for the nonlocal Gross-Pitaevskii equation with quadratic potential.

Shapovalov, Alexander, Trifonov, Andrey, Lisok, Alexander (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.

Lucie Baudouin (2005)

Revista Matemática Complutense

We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and...

Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.

Zaouch, Fouzi (2005)

Abstract and Applied Analysis

Existence, multiplicity and profile of sign-changing clustered solutions of a semiclassical nonlinear Schrödinger equation

Teresa D'Aprile, Angela Pistoia (2009)

Annales de l'I.H.P. Analyse non linéaire

Existence of weak solutions for quasilinear elliptic equations involving the $p$ -Laplacian.

Severo, Uberlandio (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique

Anne de Bouard, Arnaud Debussche (2002/2003)

Séminaire Équations aux dérivées partielles

Explosion pour l’équation de Schrödinger au régime du “log log”

Nicolas Burq (2005/2006)

Séminaire Bourbaki

On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger $L^{2}$ critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme $L^{2}$ est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.

Exponential of a hamiltonian in large subsets of a lattice and applications

J. Nourrigat (2005)

Journées Équations aux dérivées partielles

Exponential Sums and Nonlinear Schrödinger Equations.

J. Bourgain (1993)

Geometric and functional analysis

Currently displaying 1 – 15 of 15

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